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@@ -23,11 +23,11 @@ The WKB approximation is used to describe a particle of mass $m$ in a one-dimens
If $E > V(x)$, then the particle will always have an energy larger than the potential at any point $x$. Hence, there will always be some non-zero kinetic energy at every point $x$. As a consequence, the particle will continuously move in one direction (determined by the initial velocity). This happens irrespective of the potential shape: for example, it does not matter whether the potential is smooth or changes abruptly.
![Classical particle with energy smaller than potential energy](figures/classical_scat2.svg)
![Classical particle with energy smaller than potential energy](figures/classical_scat1.svg)
If $E < V(x)$, a classical particle will reach a maximum position $x_0$ such that $E = V(x_0)$ and the kinetic energy becomes zero. Then, the particle will be reflected. Again, this will happen for any potential shape.
![Classical particle with energy larger than potential energy](figures/classical_scat1.svg)
![Classical particle with energy larger than potential energy](figures/classical_scat2.svg)
In summary, in classical mechanics the global motion of a particle in a 1D potential is only determined by the value of the total energy compared to the potential $V(x)$.
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